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Solving Polynomial Equation Systems I
Author: Teo Mora
Publisher: Cambridge University Press
Published: 2003-03-27
Total Pages: 0
ISBN-13: 9780521811545
DOWNLOAD EBOOK →With the advent of computers, theoretical studies and solution methods for polynomial equations have changed dramatically. Many classical results can be more usefully recast within a different framework which in turn lends itself to further theoretical development tuned to computation. This first book in a trilogy is devoted to the new approach. It is a handbook covering the classical theory of finding roots of a univariate polynomial, emphasizing computational aspects, especially the representation and manipulation of algebraic numbers, enlarged by more recent representations like the Duval Model and the Thom Codification. Mora aims to show that solving a polynomial equation really means finding algorithms that help one manipulate roots rather than simply computing them; to that end he also surveys algorithms for factorizing univariate polynomials.
Solving Polynomial Equation Systems I
Author: Teo Mora
Publisher: Cambridge University Press
Published: 2003-03-27
Total Pages: 452
ISBN-13: 9780521811545
DOWNLOAD EBOOK →Computational algebra; computational number theory; commutative algebra; handbook; reference; algorithmic; modern.
Solving Systems of Polynomial Equations
Author: Bernd Sturmfels
Publisher: American Mathematical Soc.
Published: 2002
Total Pages: 162
ISBN-13: 0821832514
DOWNLOAD EBOOK →Bridging a number of mathematical disciplines, and exposing many facets of systems of polynomial equations, Bernd Sturmfels's study covers a wide spectrum of mathematical techniques and algorithms, both symbolic and numerical.
Solving Polynomial Equation Systems IV: Volume 4, Buchberger Theory and Beyond
Author: Teo Mora
Publisher: Cambridge University Press
Published: 2016-04-01
Total Pages: 833
ISBN-13: 1316381382
DOWNLOAD EBOOK →In this fourth and final volume the author extends Buchberger's Algorithm in three different directions. First, he extends the theory to group rings and other Ore-like extensions, and provides an operative scheme that allows one to set a Buchberger theory over any effective associative ring. Second, he covers similar extensions as tools for discussing parametric polynomial systems, the notion of SAGBI-bases, Gröbner bases over invariant rings and Hironaka's theory. Finally, Mora shows how Hilbert's followers - notably Janet, Gunther and Macaulay - anticipated Buchberger's ideas and discusses the most promising recent alternatives by Gerdt (involutive bases) and Faugère (F4 and F5). This comprehensive treatment in four volumes is a significant contribution to algorithmic commutative algebra that will be essential reading for algebraists and algebraic geometers.
Solving Polynomial Equation Systems
Author: Teo Mora
Publisher:
Published: 2003
Total Pages: 439
ISBN-13: 9780511178887
DOWNLOAD EBOOK →Mora covers the classical theory of finding roots of a univariate polynomial, emphasising computational aspects. He shows that solving a polynomial equation really means finding algorithms that help one manipulate roots rather than simply computing them; to that end he also surveys algorithms for factorizing univariate polynomials.
Solving Polynomial Equation Systems II
Author: Teo Mora
Publisher: Cambridge University Press
Published: 2003
Total Pages: 792
ISBN-13: 9780521811569
DOWNLOAD EBOOK →This volume focuses on Buchberger theory and its application to the algorithmic view of commutative algebra. The presentation is based on the intrinsic linear algebra structure of Groebner bases, and thus elementary considerations lead easily to the state-of-the-art in its algorithmization.
Solving Polynomial Equation Systems I
Author: Teo Mora
Publisher:
Published: 2003
Total Pages: 0
ISBN-13: 9780511306020
DOWNLOAD EBOOK →Mora covers the classical theory of finding roots of a univariate polynomial, emphasising computational aspects. He shows that solving a polynomial equation really means finding algorithms that help one manipulate roots rather than simply computing them; to that end he also surveys algorithms for factorizing univariate polynomials.
Solving Systems of Polynomial Equations
Author: Bernd Sturmfels
Publisher: American Mathematical Soc.
Published: 2002
Total Pages: 162
ISBN-13: 0821832514
DOWNLOAD EBOOK →Bridging a number of mathematical disciplines, and exposing many facets of systems of polynomial equations, Bernd Sturmfels's study covers a wide spectrum of mathematical techniques and algorithms, both symbolic and numerical.
Numerically Solving Polynomial Systems with Bertini
Author: Daniel J. Bates
Publisher: SIAM
Published: 2013-11-08
Total Pages: 372
ISBN-13: 1611972701
DOWNLOAD EBOOK →This book is a guide to concepts and practice in numerical algebraic geometry ? the solution of systems of polynomial equations by numerical methods. Through numerous examples, the authors show how to apply the well-received and widely used open-source Bertini software package to compute solutions, including a detailed manual on syntax and usage options. The authors also maintain a complementary web page where readers can find supplementary materials and Bertini input files. Numerically Solving Polynomial Systems with Bertini approaches numerical algebraic geometry from a user's point of view with numerous examples of how Bertini is applicable to polynomial systems. It treats the fundamental task of solving a given polynomial system and describes the latest advances in the field, including algorithms for intersecting and projecting algebraic sets, methods for treating singular sets, the nascent field of real numerical algebraic geometry, and applications to large polynomial systems arising from differential equations. Those who wish to solve polynomial systems can start gently by finding isolated solutions to small systems, advance rapidly to using algorithms for finding positive-dimensional solution sets (curves, surfaces, etc.), and learn how to use parallel computers on large problems. These techniques are of interest to engineers and scientists in fields where polynomial equations arise, including robotics, control theory, economics, physics, numerical PDEs, and computational chemistry.
